# Learning Explicit Single-Cell Dynamics Using ODE Representations

arXiv: https://arxiv.org/abs/2510.02903 · HTML: https://mlsanity.com/paper/2510.02903/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 66 references that are in the map.
- First posted on arXiv 3 Oct 2025.

## Builds on (most cited first, 25 of 25)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [Neural Operator: Learning Maps Between Function Spaces](https://mlsanity.com/paper/2108.08481/) (2021)
- [TrajectoryNet: A Dynamic Optimal Transport Network for Modeling Cellular Dynamics](https://mlsanity.com/paper/2002.04461/) (2020)
- [Action Matching: Learning Stochastic Dynamics from Samples](https://mlsanity.com/paper/2210.06662/) (2022)
- [Simulation-free Schr"odinger bridges via score and flow matching](https://mlsanity.com/paper/2307.03672/) (2023)
- [Metric Flow Matching for Smooth Interpolations on the Data Manifold](https://mlsanity.com/paper/2405.14780/) (2024)
- [Manifold Interpolating Optimal-Transport Flows for Trajectory Inference](https://mlsanity.com/paper/2206.14928/) (2022)
- [ODEFormer: Symbolic Regression of Dynamical Systems with Transformers](https://mlsanity.com/paper/2310.05573/) (2023)
- [A Computational Framework for Solving Wasserstein Lagrangian Flows](https://mlsanity.com/paper/2310.10649/) (2023)
- [Learning stochastic dynamics from snapshots through regularized unbalanced optimal transport](https://mlsanity.com/paper/2410.00844/) (2024)
- [Towards a mathematical theory of trajectory inference](https://mlsanity.com/paper/2102.09204/) (2021)
- [Marrying Causal Representation Learning with Dynamical Systems for Science](https://mlsanity.com/paper/2405.13888/) (2024)
- [Learning diffusion at lightspeed](https://mlsanity.com/paper/2406.12616/) (2024)
- [Joint Velocity-Growth Flow Matching for Single-Cell Dynamics Modeling](https://mlsanity.com/paper/2505.13413/) (2025)
- [Mechanistic Neural Networks for Scientific Machine Learning](https://mlsanity.com/paper/2402.13077/) (2024)
- [Interpretable Neural ODEs for Gene Regulatory Network Discovery under Perturbations](https://mlsanity.com/paper/2501.02409/) (2025)
- [Learning Control-Oriented Dynamical Structure from Data](https://mlsanity.com/paper/2302.02529/) (2023)
- [Scalable Mechanistic Neural Networks for Differential Equations and Machine Learning](https://mlsanity.com/paper/2410.06074/) (2024)
- [Recovering Time-Varying Networks From Single-Cell Data](https://mlsanity.com/paper/2410.01853/) (2024)

## Built on by (most cited first, 1 of 1)

- [Learning Latent Dynamical Causal Processes for Single-Cell Perturbation Prediction](https://mlsanity.com/paper/2605.25581/) (2026)

## Abstract (arXiv)

Modeling the dynamics of cellular differentiation is fundamental to advancing the understanding and treatment of diseases associated with this process, such as cancer. With the rapid growth of single-cell datasets, this has also become a particularly promising and active domain for machine learning. Current state-of-the-art models, however, rely on computationally expensive optimal transport preprocessing and multi-stage training, while also not discovering explicit gene interactions. To address these challenges we propose Cell-Mechanistic Neural Networks (Cell-MNN), an encoder-decoder architecture whose latent representation is a locally linearized ODE governing the dynamics of cellular evolution from stem to tissue cells. Cell-MNN is fully end-to-end (besides a standard PCA pre-processing) and its ODE representation explicitly learns biologically consistent and interpretable gene interactions. Empirically, we show that Cell-MNN achieves competitive performance on single-cell benchmarks, surpasses state-of-the-art baselines in scaling to larger datasets and joint training across multiple datasets, while also learning interpretable gene interactions that we validate against the TRRUST database of gene interactions.